I have the following summary of data point values:

Under 600: 38%
601-800: 51%
Over 801: 11%

Assuming a normal distribution of values, how can I calculate the mean?

Note: it doesn't have to be precise, just a rough estimation to the nearest 10 would be sufficient.

Many thanks!


closed as off-topic by Michael Chernick, kjetil b halvorsen, mdewey, Stephan Kolassa, Peter Flom Oct 16 '17 at 12:22

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  • 2
    $\begingroup$ This reads like a routine textbook exercise ... is this an exercise for some class? $\endgroup$ – Glen_b Oct 15 '17 at 20:32
  • $\begingroup$ Since this seems like homework, here's a hint. The median is the same as the mean in a normal distribution. $\endgroup$ – Peter Flom Oct 16 '17 at 12:22
  • $\begingroup$ No the reason I am asking this question is that I have access to some room rental data from a lettings website and while they don't show the average room price they do show room prices ranges (as listed in the question). So assuming normal distribution (which isn't a correct assumption but workable given the context) I wanted to know what formula I can use to calculate the mean. If there's some other way in which I am meant to ask the question please let me know. $\endgroup$ – Charlie Reay Oct 17 '17 at 9:12

Interesting question... I'd start with a standard normal table like this one. The only real info you have is the place on the distribution of the numbers 600 and 800. They lie at CDF values of 38% and 89% respectively. The corresponding z scores are -0.31, and 1.23. So that means that the values 600 and 800 are 1.54 SD apart from each other. Since they are 200 apart from each other in score, the SD must be 200/1.54 ~= 130. To get from a z-score of -0.31 to the z-score of zero (the mean), you must add 0.31 SDs, or ~ 40. So the mean is 40 above 600, or 640.

Hope that helps!


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